Pm Cs1 m Monoclinic No. 6 P1m1 Patterson symmetry P12/m1 UNIQUE AXIS b

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1

Symmetry operations

 (1)  1 (2)  m   x, 0, z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 c 1
 (1) x, y, z (2) x, -y, z
no conditions
Special: as above, plus
 1 b m
 x, 1/2, z
no extra conditions
 1 a m
 x, 0, z
no extra conditions

Symmetry of special projections

 Along [001]   p11ma' = ap   b' = b   Origin at 0, 0, z Along [100]   p1m1a' = b   b' = cp   Origin at x, 0, 0 Along [010]   p1a' = c   b' = a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb [2] P1c1 (c' = 2c) (Pc, 7); [2] P1a1 (a' = 2a) (Pc, 7); [2] B1e1 (a' = 2a, c' = 2c) (Pc, 7); [2] C1m1 (a' = 2a, b' = 2b) (Cm, 8); [2] A1m1 (b' = 2b, c' = 2c) (Cm, 8); [2] F1m1 (a' = 2a, b' = 2b, c' = 2c) (Cm, 8)

Maximal isomorphic subgroups of lowest index

 IIc [2] P1m1 (b' = 2b) (Pm, 6); [2] P1m1 (c' = 2c or a' = 2a or a' = a + c, c' = -a + c) (Pm, 6)

Minimal non-isomorphic supergroups

 I [2] P2/m (10); [2] P21/m (11); [2] Pmm2 (25); [2] Pmc21 (26); [2] Pma2 (28); [2] Pmn21 (31); [2] Amm2 (38); [2] Ama2 (40); [3] P-6 (174)
 II [2] C1m1 (Cm, 8); [2] A1m1 (Cm, 8); [2] I1m1 (Cm, 8)

 Pm Cs1 m Monoclinic No. 6 P11m Patterson symmetry P112/m UNIQUE AXIS c

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/2

Symmetry operations

 (1)  1 (2)  m   x, y, 0

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 c 1
 (1) x, y, z (2) x, y, -z
no conditions
Special: as above, plus
 1 b m
 x, y, 1/2
no extra conditions
 1 a m
 x, y, 0
no extra conditions

Symmetry of special projections

 Along [001]   p1a' = a   b' = b   Origin at 0, 0, z Along [100]   p11ma' = bp   b' = c   Origin at x, 0, 0 Along [010]   p1m1a' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb [2] P11a (a' = 2a) (Pc, 7); [2] P11b (b' = 2b) (Pc, 7); [2] C11e (a' = 2a, b' = 2b) (Pc, 7); [2] A11m (b' = 2b, c' = 2c) (Cm, 8); [2] B11m (a' = 2a, c' = 2c) (Cm, 8); [2] F11m (a' = 2a, b' = 2b, c' = 2c) (Cm, 8)

Maximal isomorphic subgroups of lowest index

 IIc [2] P11m (c' = 2c) (Pm, 6); [2] P11m (a' = 2a or b' = 2b or a' = a - b, b' = a + b) (Pm, 6)

Minimal non-isomorphic supergroups

 I [2] P2/m (10); [2] P21/m (11); [2] Pmm2 (25); [2] Pmc21 (26); [2] Pma2 (28); [2] Pmn21 (31); [2] Amm2 (38); [2] Ama2 (40); [3] P-6 (174)
 II [2] A11m (Cm, 8); [2] B11m (Cm, 8); [2] I11m (Cm, 8)